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| [[Bild:KovarianteAbleitung.png]] | | [[Bild:KovarianteAbleitung.png]] |
| <source lang="latex"> | | <source lang="latex"> |
| \begin{align}
| | T_{rs...;l}^{ik...} = T_{rs...,l}^{ik...}&+ \Gamma _{ml}^{i}T_{rs...}^{mk...}\quad&&+\Gamma _{ml}^{i}T_{is...}^{rm...}... &\quad&\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index} \\ |
| T_{{\color{Orange}rs...}; \color{Red}l}^{\color{Blue}ik...} | | & +\Gamma _{rl}^{m}T_{ms...}^{ik...}\quad&&+\Gamma _{rl}^{m}T_{rm...}^{ik...}...&&\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index} \\ |
| = | |
| T_{{\color{Orange}rs...}, \color{Red}l}^{\color{Blue} ik...}& | |
| +
| |
| \Gamma _{ m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{m\color{Blue}k...}\quad&& | |
| +
| |
| \Gamma _{m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{{\color{Blue}r}m\color{Blue}...}... &\quad& | |
| {\color{Blue}\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}} \\
| |
| & + | |
| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{m\color{Orange}s...}^{ \color{Blue}ik...}\quad&& | |
| + | |
| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{{\color{Orange}r}m\color{Orange}...}^{ \color{Blue}ik...}...&& | |
| \color{Orange}{\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}} \\
| |
| \end{align}
| |
| </source> | | </source> |
|
| |
|
| :<math>
| |
| \begin{align}
| |
| T_{{\color{Orange}rs...}; \color{Red}l}^{\color{Blue}ik...}
| |
| =
| |
| T_{{\color{Orange}rs...}, \color{Red}l}^{\color{Blue} ik...}&
| |
| +
| |
| \Gamma _{ m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{m\color{Blue}k...}\quad&&
| |
| +
| |
| \Gamma _{m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{{\color{Blue}r}m\color{Blue}...}... &\quad&
| |
| {\color{Blue}\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}} \\
| |
| & +
| |
| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{m\color{Orange}s...}^{ \color{Blue}ik...}\quad&&
| |
| +
| |
| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{{\color{Orange}r}m\color{Orange}...}^{ \color{Blue}ik...}...&&
| |
| \color{Orange}{\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}} \\
| |
| \end{align}
| |
| </math>
| |
|
| |
|
| | | <math> |
| :<math>
| |
| {A^{\color{Violet}\lambda }}_{{\color{Orange}\mu};{\color{Red}\nu} } | | {A^{\color{Violet}\lambda }}_{{\color{Orange}\mu};{\color{Red}\nu} } |
| = | | = |